Problem: Multiply.
$3 \times 42$ and $0.3 \times 4.2$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $3 \times 42$. Then we can estimate to place the decimal point in the product of $0.3 \times 4.2$. $\begin{aligned} 42&\\ \underline{ \times 3}&\\ 6}\\ \underline{+120}}\\ 126 \end{aligned}$ Let's estimate to place the decimal in $0.3 \times 4.2$. $\begin{aligned} 0.3 \times 4.2 &\approx 0.3 \times 4\\\\ &\approx \dfrac{3}{10}\times \dfrac{4}{1}\\\\ &\approx \dfrac{12}{10}\\\\ &\approx 1.2 \end{aligned}$ Where can we place the decimal in $126$ to get a product close to $1.2$ ? $1.26 = 0.3 \times 4.2$